Question

Answer the following questions:
(a) Define electric flux. Write its $SI$ unit.
(b) "Gauss's law in electrostatics is true for any closed surface, no matter what its shape or size is." Justify this statement with the help of a suitable example.

Answer 1

(a)

Electric Flux through a surface is defined as the surface integral of the electric field lines passing normally through the surface.

$\varphi =\int \overrightarrow{E}.\overrightarrow{dS}$

According to gauss's law, total electric flux through a closed surface equals the net charge enclosed in the surface divided by the permittivitty.

Consider a point charge q. Its net electric flux through any closed surface enlcosing it will be be equal to $\varphi =\frac{q}{{\epsilon }_o}$. This is independent of the choice of the shape and size of the closed surface.

The SI unit of electric flux is Volt - metres (V m)

(b)

For charged spherical shell, all charge lies on the outer circumference of the surface.

Consider a charged spherical shell with outer radius b and inner radius a. The charge resides at a radius b from the centre. Consider a gaussian surface of radius $a<r<b$. Charge enclosed in this guassian surface will be zero.

Using gauss's law,

$\int E.ds=\frac{q_{enclosed}}{{\epsilon }_o}$

$E\times 2\pi rdr=0$

$E=0$